A MATHEMATICAL-MODEL OF INSULIN-SECRETION

Diabetes mellitus is a chronic state of excessive blood glucose levels (hyperglycaemia), which may result from many environmental and geneti c factors, often acting jointly. The major regulator of glucose concen tration in the blood is insulin. It is known that about 50% of the ins ulin is taken up by the liver on passing through it after secretion fr om the pancreas. The precise value of this fractional uptake is not kn own, so the prehepatic insulin secretion rates cannot be readily estim ated from the plasma insulin concentration levels. By utilizing the eq uimolar secretion of insulin and connecting peptide (C-peptide) from t he pancreas, a noninvasive method has been formulated. This was based on a compartmental model which involved the pancreas, liver, and plasm a. The resulting differential equation yielded a gamma variate solutio n which could be readily linearized. The model was then tested on 56 n ormal (51 nonobese and 5 obese) subjects, and three groups of subjects with diabetes who could be labelled as mild, moderate, and severe (ba sed on the fasting plasma glucose concentration) with 83, 88, and 64 s ubjects respectively. We have focused on the human patient environment of the clinician to produce a distinct model which gave a consistent pattern within all four groups with good fits between observed and the oretical values of the plasma insulin levels. The consequent rates for insulin secretion were consistent across the groups and were clinical ly meaningful.